{"id":1179288,"date":"2026-07-21T09:31:39","date_gmt":"2026-07-21T16:31:39","guid":{"rendered":"https:\/\/research.codeghost.online\/en-us\/research\/publication\/reinforce-ada-an-adaptive-sampling-framework-under-non-linear-rl-objectives\/"},"modified":"2026-07-22T17:05:59","modified_gmt":"2026-07-23T00:05:59","slug":"reinforce-ada-an-adaptive-sampling-framework-under-non-linear-rl-objectives","status":"publish","type":"msr-research-item","link":"https:\/\/research.codeghost.online\/en-us\/research\/publication\/reinforce-ada-an-adaptive-sampling-framework-under-non-linear-rl-objectives\/","title":{"rendered":"Reinforce-Ada: An Adaptive Sampling Framework under Non-linear RL Objectives"},"content":{"rendered":"\n\n\n<p class=\"wp-block-paragraph\">Reinforcement learning (RL) for large language model reasoning is frequently hindered by signal loss, a phenomenon where standard uniform sampling with small group sizes fails to uncover informative learning signals for difficult prompts. We demonstrate that this collapse is a statistical artifact of undersampling rather than an inherent model limitation. To address this systematically, we introduce a theoretical framework based on optimizing a non-linear RL objective (e.g., log-likelihood). We show that this objective naturally induces a weighted gradient estimator that prioritizes difficult prompts, which can be robustly realized through adaptive sampling. Guided by this framework, we propose Reinforce-Ada, a family of algorithms that dynamically allocates inference budgets based on prompt difficulty, effectively scaling up RL compute to where it is needed most. Unlike passive filtering methods that discard low-signal prompts, Reinforce-Ada actively invests compute to recover them. We introduce two efficient realizations: an estimation-based approach and a model-free sequential sampling approach. Extensive experiments across multiple benchmarks show that Reinforce-Ada significantly outperforms uniform baselines like GRPO, recovering lost signals and accelerating convergence by up to <math><mrow><mn>2<\/mn><mo>\u00d7<\/mo><\/mrow><\/math> while maintaining the same total inference budget. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Reinforcement learning (RL) for large language model reasoning is frequently hindered by signal loss, a phenomenon where standard uniform sampling with small group sizes fails to uncover informative learning signals for difficult prompts. We demonstrate that this collapse is a statistical artifact of undersampling rather than an inherent model limitation. To address this systematically, we [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"text","value":"Wei Xiong","user_id":0},{"type":"text","value":"Chenlu Ye","user_id":0},{"type":"text","value":"Baohao Liao","user_id":0},{"type":"user_nicename","value":"Hanze Dong","user_id":"43925"},{"type":"user_nicename","value":"Xinxing Xu","user_id":"43941"},{"type":"text","value":"Christof Monz","user_id":0},{"type":"user_nicename","value":"Jiang Bian","user_id":"38481"},{"type":"user_nicename","value":"Nan Jiang","user_id":"36614"},{"type":"text","value":"Tong 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